Key points are not available for this paper at this time.
A new three-dimensional computational method for obtaining structures of a rapidly rotating star and multiple star systems, including binaries, is formulated to calculate many kinds of structures, such as ellipsoids, dumbbells, and deep contact binaries. Four kinds of multibody systems including two-body binary, three-body, four-body, and five-body systems are computed; they are assumed to be rigidly rotating and composed of equal masses. For binary systems, the equilibrium sequences from ellipsoid to binary through dumbbell structure are computed for two kinds of equation of state: polytropic stars and zero-temperature white dwarfs. Three- and four-body systems become a three-lobed or a four-lobed configuration as the fluids come into contact, but a five-body system becomes a one-ring configuration finally. This implies that the five-body sequence bifurcates from the one-ring sequence, although two-, three-, and four-body sequences bifurcate from the spheroidal sequence.
Izumi Hachisu (Sat,) studied this question.